PayPal claim filed against me. What to do?

So basically,
I sold wheels.
Buyer pays with PayPal.
Buyer chose UPS to ship the wheels.
I shipped wheels with UPS.
UPS lost 2 of the wheels.
I file a claim for the buyer with UPS.
Buyer files a claim with PayPal.
In the buyer's statement, he says that I ignored his texts and did little to nothing to contact UPS and find the wheels. (The lady that helped me file the claim with UPS knew what I was calling for every time I called and heard my name. I also have answered every text he has sent and even tried calling him about the status of the wheels.)

The dispute isn't settled yet, but when I actually talked to a PayPal rep in the claims dept., she said that I would probably have to give the buyer a full refund or take back the 2 wheels and give a partial refund.

I feel like I did everything right as a seller. I even gave him a choice of which shipper to use. I gave him tracking numbers the minute I got them. He never asked for any kind of insurance, so I didn't offer or obtain any quotes regarding insurance.

Is there anything I can do to help my case? I have all conversations with the buyer (via text and vortex pm's) and receipts from UPS.